Regularization methods for elliptic quasi-variational inequalities in Banach spaces

In this paper, we deal with a class of ill-posed quasi-variational inequalities with contaminated data by employing the elliptic regularization in Banach spaces. Firstly, we get an existence result for quasi-variational inequalities and show that the sequence of bounded regularized solutions converg...

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Bibliographic Details
Published in:Optimization 2021-11, Vol.70 (11), p.2427-2439
Main Authors: Su, Guangwang, Xue, Guangming, Xia, Guoen, Bin, Maojun
Format: Article
Language:English
Subjects:
Banach spaces
Coercivity
coercivity conditions
Estimates
Inequalities
mosco convergence
quasi-variational inequalities
Regularization
Regularization methods
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Summary:In this paper, we deal with a class of ill-posed quasi-variational inequalities with contaminated data by employing the elliptic regularization in Banach spaces. Firstly, we get an existence result for quasi-variational inequalities and show that the sequence of bounded regularized solutions converges strongly to a solution of the original quasi-variational inequalities under mild coercivity conditions. Next, we give the boundedness of regularized solutions for quasi-variational inequalities. Finally, an example is presented to illustrate our main results.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2020.1783540